Quasi-Töplitz functions in KAM theorem

Abstract

We define and describe the class of Quasi-Töplitz functions. We then prove an abstract KAM theorem where the perturbation is in this class. We apply this theorem to a Non-Linear-Scrödinger equation on the torus $T^d$, thus proving existence and stability of quasi-periodic solutions and recovering the results of [10]. With respect to that paper we consider only the NLS which preserves the total Momentum and exploit this conserved quantity in order to simplify our treatment.

34 pages, 1 figure

Cited by in corpus (9)

• A KAM algorithm for the resonant non--linear Schrödinger equation
• KAM for reversible derivative wave equations
• An abstract Nash-Moser theorem and quasi-periodic solutions for NLW and NLS on compact Lie groups and homogeneous manifold
• KAM for beating solutions of the quintic NLS
• Growth of Sobolev norms for the quintic NLS on ${\mathbb{T}}^2$
• 1d Quantum Harmonic Oscillator Perturbed by a Potential with Logarithmic Decay
• Long time stability of small finite gap solutions of the cubic Nonlinear Schrödinger equation on ${\mathbb{T}}^2$
• Reducible quasi-periodic solutions for the Non Linear Schrödinger equation
• A KAM result on compact Lie groups